How do you write y = | x - 2| as piecewise functions?

Dec 26, 2017

See a solution process below:

Explanation:

Step 1) First, solve the term within the absolute value function for $0$:

$x - 2 = 0$

$x - 2 + \textcolor{red}{2} = 0 + \textcolor{red}{2}$

$x - 0 = 2$

$x = 2$

Step 2) Multiply the term within the absolute value function by $- 1$ and write a "less than" inequality with the result of Step 1:

$- 1 \left(x - 2\right) \implies - x + 2$

$y = - x + 2 \text{ for } x < 2$

Step 3) Take the term within the absolute value function and write a "greater than or equal to" inequality with the result of Step 1:

$y = x - 2 \text{ for } x \ge 2$

Step 4) Combine Step 2 & Step 3 to form the piecewise function:

$y = \left\{- x + 2 \text{ for "x < 2; x - 2" for } x \ge 2\right\}$

Dec 26, 2017

see below

Explanation:

f: y=|x−2|

${f}_{1} : y = x$
${f}_{2} : y = | x |$
${f}_{3} : y = | x - 2 |$

Absolute value mirrors every negative value to the positive according to x axis.
And finally, a number inside absolute value moves graph to the right or left. When it's minus:$| x - 2 |$ then it moves to the right. You can remember it by finding zero point, which is 2 and it's greater than zero(on the right from zero). Now you should be able to make a graph